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Iterative solution of large linear systems /
Iterative Solution of Large Linear Systems.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1971.
|
| Colección: | Computer science and applied mathematics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Iterative Solution of Large Linear Systems; Copyright Page; Dedication; Table of Contents; Preface; Acknowledgments; Notation; List of Fundamental Matrix Properties; List of Iterative Methods; Chapter 1. Introduction; 1.1. The Model Problem; Supplementary Discussion; Exercises; Chapter 2. Matrix Preliminaries; 2.1. Review of Matrix Theory; 2.2. Hermitian Matrices and Positive Definite Matrices; 2.3. Vector Norms and Matrix Norms; 2.4. Convergence of Sequences of Vectors and Matrices; 2.5. Irreducibility and Weak Diagonal Dominance; 2.6. Property A.
- 2.7. L-Matrices and Related Matrices2.8. Illustrations; Supplementary Discussion; Exercises; Chapter 3. Linear Stationary Iterative Methods; 3.1. Introduction; 3.2. Consistency, Reciprocal Consistency, and Complete Consistency; 3.3. Basic Linear Stationary Iterative Methods; 3.4. Generation of Completely Consistent Methods; 3.5. General Convergence Theorems; 3.6. Alternative Convergence Conditions; 3.7. Rates of Convergence; 3.8. The Jordan Condition Number of a 2 � 2 Matrix; Supplementary Discussion; Exercises; Chapter 4. Convergence of the Basic Iterative Methods.
- 4.1. General Convergence Theorems4.2. Irreducible Matrices with Weak Diagonal Dominance; 4.3. Positive Definite Matrices; 4.4. The SOR Method with Varying Relaxation Factors; 4.5. L-Matrices and Related Matrices; 4.6. Rates of Convergence of the J and GS Methods for the Model Problem; Supplementary Discussion; Exercises; Chapter 5. Eigenvalues of the SOR Method for Consistently Ordered Matrices; 5.1. Introduction; 5.2. Block Tri-Diagonal Matrices; 5.3. Consistently Ordered Matrices and Ordering Vectors; 5.4. Property A; 5.5. Nonmigratory Permutations.
- 6.6. Iterative Methods of Choosing [omega]b 6.7. An Upper Bound for [mu]; 6.8. A Priori Determination of [mu]: Exact Methods; 6.9. A Priori Determination of [mu]: Approximate Values; 6.10. Numerical Results; Supplementary Discussion; Exercises; Chapter 7. Norms of the SOR Method; 7.1. The Jordan Canonical Form of L[omega]; 7.2. Basic Eigenvalue Relation; 7.3. Determination of L[omega] D; 7.4. Determination of L[omega] D; 7.5. Determination of L[omega] A; 7.6. Determination of L[omega] A; 7.7. Comparison of L[omega]mb D and L[omega]mb IIA; Supplementary Discussion; Exercises; Chapter 8. The Modified SOR Method: Fixed Parameters.